Multiple part post:
First: Connect or not: If you have a good 3-stage converter then by all means hook up.. This is the BEST way to maintain your batteries when the RV is not in use.. ON the other hand there are some downright crappy converters out there.
Now 15/20/30 or 50 amps?
Fifteen or 20 amps (Standard Duplex outlets are either 15 or 15/20) is good for battery maintenance and a few things related.. But don't try to run Big Ticket items on 15 amps. you can run one on 20
(Big ticket = anything over 1,000 watts, Water heater, A/C. Space heaters or Cheap heat or heat strips, Microwave) Many Vacuum cleaners.
30 amps you can run two big ticket but only one of them can be an A/C but. I Seriously do not recommend 30 amp for homes less you personally know how to install it (I did).
50 amp is all the power you can eat If you have an electrician install. Go with 50.
Why the dislike for professionally installed 30 amp?
I have read far too many threads here which start almost exactly the same "I had an electrician install a 30 amp outlet and------"
(Or friend, one RV owner did his own)
30 amp outlets are 120 volt, Same as the 15/20 type. BUT they LOOK like a very popular 240 volt outlet used for Dryers, or Welders or other shop hardware. Of courese it says right on the thing it is for 125 volt use max.. but I've never met an electrician who actually read the lettering on the device.. they just "Know" how to hook it up.
With 50 amp outlets this is not a problem,, They really do know how to hook them up correctly.
Home is where I park it!